Pertanyaan

Tentukan turunan pertama fungsi berikut, sederhanakan jika mungkin. 1 . y = ( sin − 1 x ) 2

Tentukan turunan pertama fungsi berikut, sederhanakan jika mungkin.

$1$ . $y = (sin^{- 1} x)^{2}$

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Teorema turunan fungsi invers trigonometri. Diperoleh turunan pertamanya yaitu: Maka,turunan pertama fungsi adalah .

Teorema turunan fungsi invers trigonometri.

$fraction numerator d over denominator d x end fraction open square brackets sin to the power of negative 1 end exponent space x close square brackets equals fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction$

Diperoleh turunan pertamanya yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row y equals cell open parentheses sin to the power of negative 1 end exponent space x close parentheses squared end cell row cell y apostrophe end cell equals cell open parentheses fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction close parentheses squared end cell row blank equals cell fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction times fraction numerator 1 over denominator square root of 1 minus x squared end root end fraction end cell row blank equals cell fraction numerator 1 over denominator 1 minus x squared end fraction end cell end table$

Maka, turunan pertama fungsi y equals open parentheses sin to the power of negative 1 end exponent space x close parentheses squared adalah $y apostrophe equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 1 over denominator 1 minus x squared end fraction end cell end table$ .